82 citations · 566 across the 38 of their papers we have counts for
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Random Matrices with Merging Singularities and the Painlevé V Equation
Tom Claeys, Benjamin Fahs
We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form $\frac{1}{Z_n} \big|\det \big( M^2-tI \big)\big|^α e^{-…
Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
Alexander Bogatskiy, Tom Claeys, Alexander Its
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a discontinuous Gaussian weight, in a critical regime where the discontinuity is close to…
Correlation kernels for sums and products of random matrices
Tom Claeys, Arno B. J. Kuijlaars, Dong Wang
Let be a random matrix whose squared singular value density is a polynomial ensemble. We derive double contour integral formulas for the correlation kernels of the squared sing…
Random matrix ensembles with singularities and a hierarchy of Painlevé III equations
Max R. Atkin, Tom Claeys, Francesco Mezzadri
We study unitary invariant random matrix ensembles with singular potentials. We obtain asymptotics for the partition functions associated to the Laguerre and Gaussian Unitary Ensem…